Question

Find the equation of the axis symmetry:Find the x-intercept(s):and y-intercept(s):Find the coordinates of the vertex:

Answer 1

Step 1

Find the equation of the axis of symmetry

`\begin{gathered} From\text{ the graph the zeroes are} \\ x=-2 \\ \text{and} \\ x=4 \end{gathered}`
`\begin{gathered} \text{Hence the function is } \\ y=(x+2)(x-4) \\ y=x^2-4x+2x-8 \\ y=x^2-2x-8 \end{gathered}`

The equation of symmetry is given as

`\begin{gathered} x=(-b)/(2a) \\ b=-2 \\ a=1 \\ c=-8 \end{gathered}`
`\begin{gathered} x=(-(-2))/(2(1)) \\ x=(2)/(2)=1 \\ x=1 \end{gathered}`

Step 2

Find the x-intercepts

`\begin{gathered} \text{From the graph, the x-intercepts are}; \\ (4,0),(-2,0) \end{gathered}`

Step 3

Find the y-intercepts

`y\text{-intercept; (0,-8)}`

Step 4

Find the coordinates of the vertex

`The\text{ coordinates of the Vertex ; (1,-9)}`